A cloud scheme for data assimilation:: Description and initial tests

A new cloud scheme has been developed specifically for the purposes of variational data assimilation, a task complicated by the inherent nonlinearity of many cloud processes. The aim was to retain the most important features of the ECMWF nonlinear cloud scheme, while removing much of the complexity and as many of the discrete transitions as possible. The scheme thus retains a simplified link to convective detrainment, and uses a similar formulation for the production of precipitation. A flexible statistical cloud scheme approach is used, where the diagnosis of stratiform cloud fraction and condensate amount depend on assumptions concerning subgrid-scale fluctuations. A novel aspect of the new scheme is the treatment of precipitation evaporation that specifically takes this subgrid distribution of humidity variability into account. The scheme is tested by comparing physical tendencies of thermodynamical quantities, calculated for a series of input temperature and humidity profiles, to those produced by the complex prognostic cloud scheme used in the forecast model. Additionally, a series of model integrations are performed, with the full prognostic scheme used in operational forecasts replaced by the new scheme described here. In both cases, using the prognostic scheme as a metric, the new scheme improves on the current assimilation cloud scheme for many attributes such as cloud cover and ice water content, both in the tropics and midlatitudes. In particular the new diagnostic scheme addresses the overriding weakness of the current diagnostic scheme which produces almost no precipitation in the tropics. Tangent-linear (TL) and adjoint versions of the new scheme have been constructed and it is demonstrated that the scheme can successfully and robustly perform TL integrations for a 12-hour window, and significantly improves the TL approximation of the simplified linearized model to finite difference calculations using the full nonlinear forecast model.